Pisot数，Salem数和广义多项式

IF 0.6 3区数学 Q3 MATHEMATICS

Journal of Number Theory Pub Date : 2025-02-17 DOI:10.1016/j.jnt.2025.01.001

Jakub Byszewski , Jakub Konieczny

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引用次数: 0

摘要

我们研究可以由广义多项式表达式的消失来定义的整数集。我们证明了这包括Salem型线性循环序列的值集和一些Pisot型线性循环序列的值集。为此，我们在数域上引入广义多项式的概念。我们建立了线性循环序列的值集与数域的乘法群的子半群的广义多项式表达式的存在性之间的联系。

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Pisot numbers, Salem numbers, and generalised polynomials

We study sets of integers that can be defined by the vanishing of a generalised polynomial expression. We show that this includes sets of values of linear recurrent sequences of Salem type and some linear recurrent sequences of Pisot type. To this end, we introduce the notion of a generalised polynomial on a number field. We establish a connection between the existence of generalised polynomial expressions for sets of values of linear recurrent sequences and for subsemigroups of multiplicative groups of number fields.

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来源期刊

Journal of Number Theory 数学-数学

CiteScore

1.30

自引率

14.30%

发文量

122

审稿时长

16 weeks

期刊介绍： The Journal of Number Theory (JNT) features selected research articles that represent the broad spectrum of interest in contemporary number theory and allied areas. A valuable resource for mathematicians, the journal provides an international forum for the publication of original research in this field. The Journal of Number Theory is encouraging submissions of quality, long articles where most or all of the technical details are included. The journal now considers and welcomes also papers in Computational Number Theory. Starting in May 2019, JNT will have a new format with 3 sections: JNT Prime targets (possibly very long with complete proofs) high impact papers. Articles published in this section will be granted 1 year promotional open access. JNT General Section is for shorter papers. We particularly encourage submission from junior researchers. Every attempt will be made to expedite the review process for such submissions. Computational JNT . This section aims to provide a forum to disseminate contributions which make significant use of computer calculations to derive novel number theoretic results. There will be an online repository where supplementary codes and data can be stored.